A One-Dimensional Quartic Map Modeling the Aggressive Patterns of Worker Honey Bees towards a Foreign Queen: A Theoretical and Experimental Approach
by
Suzanne Sumner
Mary Washington College
Coauthors: Wyatt A. Mangum

Queen honey bees are replaced periodically to keep colonies productive. Initially the bees regard the new queen bee as foreign and will usually try to kill her. To prevent this loss, the queen bee is held in a protective cage for several days. During the introduction period, the bees display hostile behaviors on the cage collectively known as balling. The number of aggressive bees displaying this behavior (ballers) on the cage can range up to 40, but the number often decreases to zero before the queen's release; if not, the queen may be killed.

Several factors extend the duration of balling. One of these is the presence of attendant bees that accompany the queen in the cage during shipping. During queen introduction without attendant bees, the number of balling bees exhibits an exponential decay to zero. With attendants if the number of ballers decreases, the decay is usually slower. However, other aggressive and erratic patterns are also observed. With chronic balling the number of ballers never decreases to zero. With a reversion, the number decreases to zero and then dramatically increases, and either subsequently decreases to zero again or never decreases to zero (reversion and chronic balling).

These experimental results suggest a discrete model whose dependent variable is the number of bees balling the cage over time. By varying a parameter describing the intensity of aggression due to the presence of attendant bees, this model should have the following properties. Without an attendant effect, zero is an attracting fixed point on [0, 40] and convergence to it is relatively quick. With a small attendant effect, zero can still be an attractor though convergence is slower. With larger attendant effects, one or more nonzero fixed points may be present. As the attendant parameter is increased, the model undergoes the period doubling route to chaos and mimics the experimental data.

Date received: February 25, 2003